The degeneracy-locus conjecture for torsion-dense subvarieties

Let $g\in\mathbb{N}$, and let $X$ be an irreducible closed subvariety of the universal family $\mathfrak{A}_g$ defined over $\overline{\mathbb{Q}}$. Write $X_{\mathbb{C}}^{\mathrm{deg}}(1)$ for the corresponding first degeneracy locus after base change to $\mathbb{C}$. Degeneracy-locus conjecture. If $\dim X>0$ and

$$X(\overline{\mathbb{Q}})\cap\mathfrak{A}_{g,\mathrm{tors}}$$

is Zariski dense in $X$, then $X_{\mathbb{C}}^{\mathrm{deg}}(1)$ is Zariski dense in $X$. This conjecture is introduced as the condition under which the relative Manin–Mumford conjecture can be proved for all $g$; the supplied text does not establish it, so its general status remains open.